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<li><a class="reference internal" href="#"><code class="xref py py-mod docutils literal notranslate"><span class="pre">sklearn.metrics</span></code>.adjusted_rand_score</a><ul>
<li><a class="reference internal" href="#examples-using-sklearn-metrics-adjusted-rand-score">Examples using <code class="docutils literal notranslate"><span class="pre">sklearn.metrics.adjusted_rand_score</span></code></a></li>
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  <div class="section" id="sklearn-metrics-adjusted-rand-score">
<h1><a class="reference internal" href="../classes.html#module-sklearn.metrics" title="sklearn.metrics"><code class="xref py py-mod docutils literal notranslate"><span class="pre">sklearn.metrics</span></code></a>.adjusted_rand_score<a class="headerlink" href="#sklearn-metrics-adjusted-rand-score" title="Permalink to this headline">¶</a></h1>
<dl class="function">
<dt id="sklearn.metrics.adjusted_rand_score">
<code class="sig-prename descclassname">sklearn.metrics.</code><code class="sig-name descname">adjusted_rand_score</code><span class="sig-paren">(</span><em class="sig-param">labels_true</em>, <em class="sig-param">labels_pred</em><span class="sig-paren">)</span><a class="reference external" href="https://github.com/scikit-learn/scikit-learn/blob/5f3c3f037/sklearn/metrics/cluster/_supervised.py#L138"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#sklearn.metrics.adjusted_rand_score" title="Permalink to this definition">¶</a></dt>
<dd><p>Rand index adjusted for chance.</p>
<p>The Rand Index computes a similarity measure between two clusterings
by considering all pairs of samples and counting pairs that are
assigned in the same or different clusters in the predicted and
true clusterings.</p>
<p>The raw RI score is then “adjusted for chance” into the ARI score
using the following scheme:</p>
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="n">ARI</span> <span class="o">=</span> <span class="p">(</span><span class="n">RI</span> <span class="o">-</span> <span class="n">Expected_RI</span><span class="p">)</span> <span class="o">/</span> <span class="p">(</span><span class="nb">max</span><span class="p">(</span><span class="n">RI</span><span class="p">)</span> <span class="o">-</span> <span class="n">Expected_RI</span><span class="p">)</span>
</pre></div>
</div>
<p>The adjusted Rand index is thus ensured to have a value close to
0.0 for random labeling independently of the number of clusters and
samples and exactly 1.0 when the clusterings are identical (up to
a permutation).</p>
<p>ARI is a symmetric measure:</p>
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="n">adjusted_rand_score</span><span class="p">(</span><span class="n">a</span><span class="p">,</span> <span class="n">b</span><span class="p">)</span> <span class="o">==</span> <span class="n">adjusted_rand_score</span><span class="p">(</span><span class="n">b</span><span class="p">,</span> <span class="n">a</span><span class="p">)</span>
</pre></div>
</div>
<p>Read more in the <a class="reference internal" href="../clustering.html#adjusted-rand-score"><span class="std std-ref">User Guide</span></a>.</p>
<dl class="field-list simple">
<dt class="field-odd">Parameters</dt>
<dd class="field-odd"><dl class="simple">
<dt><strong>labels_true</strong><span class="classifier">int array, shape = [n_samples]</span></dt><dd><p>Ground truth class labels to be used as a reference</p>
</dd>
<dt><strong>labels_pred</strong><span class="classifier">array-like of shape (n_samples,)</span></dt><dd><p>Cluster labels to evaluate</p>
</dd>
</dl>
</dd>
<dt class="field-even">Returns</dt>
<dd class="field-even"><dl class="simple">
<dt><strong>ari</strong><span class="classifier">float</span></dt><dd><p>Similarity score between -1.0 and 1.0. Random labelings have an ARI
close to 0.0. 1.0 stands for perfect match.</p>
</dd>
</dl>
</dd>
</dl>
<div class="admonition seealso">
<p class="admonition-title">See also</p>
<dl class="simple">
<dt><a class="reference internal" href="sklearn.metrics.adjusted_mutual_info_score.html#sklearn.metrics.adjusted_mutual_info_score" title="sklearn.metrics.adjusted_mutual_info_score"><code class="xref py py-obj docutils literal notranslate"><span class="pre">adjusted_mutual_info_score</span></code></a></dt><dd><p>Adjusted Mutual Information</p>
</dd>
</dl>
</div>
<p class="rubric">References</p>
<dl class="citation">
<dt class="label" id="rab8b7c17ab82-hubert1985"><span class="brackets">Hubert1985</span></dt>
<dd><p>L. Hubert and P. Arabie, Comparing Partitions,
Journal of Classification 1985
<a class="reference external" href="https://link.springer.com/article/10.1007%2FBF01908075">https://link.springer.com/article/10.1007%2FBF01908075</a></p>
</dd>
<dt class="label" id="rab8b7c17ab82-wk"><span class="brackets">wk</span></dt>
<dd><p><a class="reference external" href="https://en.wikipedia.org/wiki/Rand_index#Adjusted_Rand_index">https://en.wikipedia.org/wiki/Rand_index#Adjusted_Rand_index</a></p>
</dd>
</dl>
<p class="rubric">Examples</p>
<p>Perfectly matching labelings have a score of 1 even</p>
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="gp">&gt;&gt;&gt; </span><span class="kn">from</span> <span class="nn">sklearn.metrics.cluster</span> <span class="kn">import</span> <span class="n">adjusted_rand_score</span>
<span class="gp">&gt;&gt;&gt; </span><span class="n">adjusted_rand_score</span><span class="p">([</span><span class="mi">0</span><span class="p">,</span> <span class="mi">0</span><span class="p">,</span> <span class="mi">1</span><span class="p">,</span> <span class="mi">1</span><span class="p">],</span> <span class="p">[</span><span class="mi">0</span><span class="p">,</span> <span class="mi">0</span><span class="p">,</span> <span class="mi">1</span><span class="p">,</span> <span class="mi">1</span><span class="p">])</span>
<span class="go">1.0</span>
<span class="gp">&gt;&gt;&gt; </span><span class="n">adjusted_rand_score</span><span class="p">([</span><span class="mi">0</span><span class="p">,</span> <span class="mi">0</span><span class="p">,</span> <span class="mi">1</span><span class="p">,</span> <span class="mi">1</span><span class="p">],</span> <span class="p">[</span><span class="mi">1</span><span class="p">,</span> <span class="mi">1</span><span class="p">,</span> <span class="mi">0</span><span class="p">,</span> <span class="mi">0</span><span class="p">])</span>
<span class="go">1.0</span>
</pre></div>
</div>
<p>Labelings that assign all classes members to the same clusters
are complete be not always pure, hence penalized:</p>
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="gp">&gt;&gt;&gt; </span><span class="n">adjusted_rand_score</span><span class="p">([</span><span class="mi">0</span><span class="p">,</span> <span class="mi">0</span><span class="p">,</span> <span class="mi">1</span><span class="p">,</span> <span class="mi">2</span><span class="p">],</span> <span class="p">[</span><span class="mi">0</span><span class="p">,</span> <span class="mi">0</span><span class="p">,</span> <span class="mi">1</span><span class="p">,</span> <span class="mi">1</span><span class="p">])</span>
<span class="go">0.57...</span>
</pre></div>
</div>
<p>ARI is symmetric, so labelings that have pure clusters with members
coming from the same classes but unnecessary splits are penalized:</p>
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="gp">&gt;&gt;&gt; </span><span class="n">adjusted_rand_score</span><span class="p">([</span><span class="mi">0</span><span class="p">,</span> <span class="mi">0</span><span class="p">,</span> <span class="mi">1</span><span class="p">,</span> <span class="mi">1</span><span class="p">],</span> <span class="p">[</span><span class="mi">0</span><span class="p">,</span> <span class="mi">0</span><span class="p">,</span> <span class="mi">1</span><span class="p">,</span> <span class="mi">2</span><span class="p">])</span>
<span class="go">0.57...</span>
</pre></div>
</div>
<p>If classes members are completely split across different clusters, the
assignment is totally incomplete, hence the ARI is very low:</p>
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="gp">&gt;&gt;&gt; </span><span class="n">adjusted_rand_score</span><span class="p">([</span><span class="mi">0</span><span class="p">,</span> <span class="mi">0</span><span class="p">,</span> <span class="mi">0</span><span class="p">,</span> <span class="mi">0</span><span class="p">],</span> <span class="p">[</span><span class="mi">0</span><span class="p">,</span> <span class="mi">1</span><span class="p">,</span> <span class="mi">2</span><span class="p">,</span> <span class="mi">3</span><span class="p">])</span>
<span class="go">0.0</span>
</pre></div>
</div>
</dd></dl>

<div class="section" id="examples-using-sklearn-metrics-adjusted-rand-score">
<h2>Examples using <code class="docutils literal notranslate"><span class="pre">sklearn.metrics.adjusted_rand_score</span></code><a class="headerlink" href="#examples-using-sklearn-metrics-adjusted-rand-score" title="Permalink to this headline">¶</a></h2>
<div class="sphx-glr-thumbcontainer" tooltip="Reference: Brendan J. Frey and Delbert Dueck, &quot;Clustering by Passing Messages Between Data Poin..."><div class="figure align-default" id="id3">
<img alt="../../_images/sphx_glr_plot_affinity_propagation_thumb.png" src="../../_images/sphx_glr_plot_affinity_propagation_thumb.png" />
<p class="caption"><span class="caption-text"><a class="reference internal" href="../../auto_examples/cluster/plot_affinity_propagation.html#sphx-glr-auto-examples-cluster-plot-affinity-propagation-py"><span class="std std-ref">Demo of affinity propagation clustering algorithm</span></a></span><a class="headerlink" href="#id3" title="Permalink to this image">¶</a></p>
</div>
</div><div class="sphx-glr-thumbcontainer" tooltip="Finds core samples of high density and expands clusters from them."><div class="figure align-default" id="id4">
<img alt="../../_images/sphx_glr_plot_dbscan_thumb.png" src="../../_images/sphx_glr_plot_dbscan_thumb.png" />
<p class="caption"><span class="caption-text"><a class="reference internal" href="../../auto_examples/cluster/plot_dbscan.html#sphx-glr-auto-examples-cluster-plot-dbscan-py"><span class="std std-ref">Demo of DBSCAN clustering algorithm</span></a></span><a class="headerlink" href="#id4" title="Permalink to this image">¶</a></p>
</div>
</div><div class="sphx-glr-thumbcontainer" tooltip="The following plots demonstrate the impact of the number of clusters and number of samples on v..."><div class="figure align-default" id="id5">
<img alt="../../_images/sphx_glr_plot_adjusted_for_chance_measures_thumb.png" src="../../_images/sphx_glr_plot_adjusted_for_chance_measures_thumb.png" />
<p class="caption"><span class="caption-text"><a class="reference internal" href="../../auto_examples/cluster/plot_adjusted_for_chance_measures.html#sphx-glr-auto-examples-cluster-plot-adjusted-for-chance-measures-py"><span class="std std-ref">Adjustment for chance in clustering performance evaluation</span></a></span><a class="headerlink" href="#id5" title="Permalink to this image">¶</a></p>
</div>
</div><div class="sphx-glr-thumbcontainer" tooltip="In this example we compare the various initialization strategies for K-means in terms of runtim..."><div class="figure align-default" id="id6">
<img alt="../../_images/sphx_glr_plot_kmeans_digits_thumb.png" src="../../_images/sphx_glr_plot_kmeans_digits_thumb.png" />
<p class="caption"><span class="caption-text"><a class="reference internal" href="../../auto_examples/cluster/plot_kmeans_digits.html#sphx-glr-auto-examples-cluster-plot-kmeans-digits-py"><span class="std std-ref">A demo of K-Means clustering on the handwritten digits data</span></a></span><a class="headerlink" href="#id6" title="Permalink to this image">¶</a></p>
</div>
</div><div class="sphx-glr-thumbcontainer" tooltip="This is an example showing how the scikit-learn can be used to cluster documents by topics usin..."><div class="figure align-default" id="id7">
<img alt="../../_images/sphx_glr_plot_document_clustering_thumb.png" src="../../_images/sphx_glr_plot_document_clustering_thumb.png" />
<p class="caption"><span class="caption-text"><a class="reference internal" href="../../auto_examples/text/plot_document_clustering.html#sphx-glr-auto-examples-text-plot-document-clustering-py"><span class="std std-ref">Clustering text documents using k-means</span></a></span><a class="headerlink" href="#id7" title="Permalink to this image">¶</a></p>
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    var navBar = document.getElementById("navbar");
    var navBarToggler = document.getElementById("sk-navbar-toggler");
    var navBarHeightHidden = "-" + navBar.getBoundingClientRect().height + "px";
    var $window = $(window);

    hideNavBar = function() {
        navBar.style.top = navBarHeightHidden;
    };

    showNavBar = function() {
        navBar.style.top = "0";
    }

    if (hashTargetOnTop()) {
        hideNavBar()
    }

    var prevScrollpos = window.pageYOffset;
    hideOnScroll = function(lastScrollTop) {
        if (($window.width() < 768) && (navBarToggler.getAttribute("aria-expanded") === 'true')) {
            return;
        }
        if (lastScrollTop > 2 && (prevScrollpos <= lastScrollTop) || hashTargetOnTop()){
            hideNavBar()
        } else {
            showNavBar()
        }
        prevScrollpos = lastScrollTop;
    };

    /*** high preformance scroll event listener***/
    var raf = window.requestAnimationFrame ||
        window.webkitRequestAnimationFrame ||
        window.mozRequestAnimationFrame ||
        window.msRequestAnimationFrame ||
        window.oRequestAnimationFrame;
    var lastScrollTop = $window.scrollTop();

    if (raf) {
        loop();
    }

    function loop() {
        var scrollTop = $window.scrollTop();
        if (lastScrollTop === scrollTop) {
            raf(loop);
            return;
        } else {
            lastScrollTop = scrollTop;
            hideOnScroll(lastScrollTop);
            raf(loop);
        }
    }
  })();
});

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